Question: $84$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $42$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 84}$ ${x = 2y-42}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-42}$ for $x$ in the first equation. ${(2y-42)}{+ y = 84}$ Simplify and solve for $y$ $ 2y-42 + y = 84 $ $ 3y-42 = 84 $ $ 3y = 126 $ $ y = \dfrac{126}{3} $ ${y = 42}$ Now that you know ${y = 42}$ , plug it back into ${x = 2y-42}$ to find $x$ ${x = 2}{(42)}{ - 42}$ $x = 84 - 42$ ${x = 42}$ You can also plug ${y = 42}$ into ${x+y = 84}$ and get the same answer for $x$ ${x + }{(42)}{= 84}$ ${x = 42}$ There were $42$ home team fans and $42$ away team fans.